Various types of liquid supply apparatus, typically inkers in various printing machines, as well as inkers and dampers in offset printing machines, utilize axially oscillating rollers which are driven from gearing on the plate cylinder of the printing machine. German Published Patent Application DE-AS 23 09 850, assigned to the assignee of the present application, describes an inker in which a plurality of milling rollers are included, all driven over a gear train from the plate cylinder. To obtain good distribution of ink on the milling rollers, some of the milling rollers are driven to oscillate in axial direction, by an axial drive. Such axial drives can be generated, for example as disclosed in German Published Patent Application DE-AS 25 14 414, by providing a separate drive mechanism for the axial movement. This can be expensive, and particularly so if the axial movement is subject to adjustment with respect to stroke of axial oscillation as well as phase position of the stroke with respect to predetermined circumferential positions of the plate cylinder.